@KoiwiGal - It depends on where you live. A lot of places do have free medical records release forms online.
But, as it says in the article, if you can't find the proper form for your location online, you can always just write a letter which clearly contains the information that they need, like name and so forth. You can definitely find out what is required for that online as family planning clinics provide the information.
It sounds like you might need to write to every place you've had a checkup, or at least every place where something significant happened that you want the records of.
Unfortunately there isn't a central registry of all your records, they are just kept with individual clinics.